Nope. I haven't used Debian in years, but just had a quick search of your problem and found that "non-free" firmware is needed and the modesetting driver appears to be used instead of the xf86-video-intel driver (the Debian "xserver-xorg-video-intel" package).

As you've seen from the script you've run, you now have DRI acceleration, so probably the first step - beyond that I've no more ideas, not having any similar hardware.

It's probably best that you examine the X.org server logs, you find some clue as to why tthe higher resolution isn't being supported if you search on any errors or warnings therein.

The other forum sees more activity, you could explain that you've now installed the firmware and try and proceed from there - but without pissing off the locals (remember that no one really owes you a "solution").

The intel forum was probably a waste of effort, that was the typical vendor's windows centric support forum. The intel Linux driver does not really have any kind of support. It's part of the kernel, you can try the kernel mailing lists - otherwise it's forums, etc. As it's a kernel issue, the problem and "solution" isn't necessarily distribution specific so it's worth searching and reading anywhere and everywhere.

Last of all you could try posting on the linuxquestions.org site, that gets more traffic and it's more likely to get you more exposure - but again how you scructure your question along with your willingess to make some effort and do some research will be a big factor. For those who do not wish to make any effort, there are proprietary, supported, operating systems or paid support.